In this work, we study the statistical behavior of entanglement of quantum bipartite systems of fermionic Gaussian states. In the literature, the degree of entanglement as measured by entanglement entropies such as von Neumann entropy, quantum purity, and Tsallis entropy has been studied over different ensembles, e.g. the Hilbert-Schmidt ensemble [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]} and the Bures-Hall ensemble [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}. Similar investigations are now being carried out over the fermionic Gaussian ensemble, where the average von Neumann entropy is obtained in [19]}. As an important step towards further understanding its statistical distribution, we aim to derive the variance. The variance describes the fluctuation of the entropy around its mean value. It also provides crucial information such as if the average entropy is typical. In addition, we study the capacity of entanglement over the fermionic Gaussian ensemble. Entanglement capacity is another entanglement measure that possesses other distinctive properties as compared to entanglement entropies [20]}.
